(225^2 - 2*225*16π + 256π^2)/(16π^2) = 16 + h^2

Answer 1

Let's simplify the left side of the equation first:

(225^2 - 2*225*16π + 256π^2)/(16π^2)

= (225^2 - 2*225*16π + 16^2 * π^2)/(16π^2)

= (225 - 16π)^2 /(16π)^2

= [(15 - 4π)(15 - 4π)] / [4*4π*π]

= (225 - 60π + 16π^2) / (16π^2)

Now, we can compare this with the right side of the equation:

16 + h^2

So, if we equate the two sides:

(225 - 60π + 16π^2) / (16π^2) = 16 + h^2

We can multiply both sides by (16π^2) to get rid of the denominator:

225 - 60π + 16π^2 = (16π^2) * (16 + h^2)

Expanding the right side:

225 - 60π + 16π^2 = 256π^2 + 16π^2h^2

Rearranging the terms:

0 = 256π^2 + 16π^2h^2 - 60π - 16π^2 - 225

Combining like terms:

0 = 16π^2h^2 - 44π - 225

Now, we have a quadratic equation in terms of h. We can solve it to find the value of h.